Modeling studies in the field have been useful to rationalize the evidences from experimental observations into theoretical, predictive, frameworks [1]}, [2]}, [3]}, [4]}. Among these theories, those addressing vertical dynamics in light-limited environments have a rich history, starting from the introduction of the concept of critical depth by Gran and Braarud [5]}, which lead to Sverdrup's celebrated critical depth hypothesis [6]}.
The idea is that phytoplankton blooms would only be possible when the mixed layer, the weakly stratified upper part of the water column, is shallower than a certain critical depth, defined as the point where the population depth-integrated gains (due to photosynthesis) surpass the depth-integrated losses (due to grazing and respiration). Sverdrup's reasoning relies on several assumptions: a well-mixed fluid layer; negligible nutrient limitations; direct proportionality between the photosynthetic biomass production and the available energy from the incoming radiation; a constant light attenuation coefficient throughout the water column.
Building on such ideas, and aiming to improve realism, subsequent studies started to address also the role of algal self-shading [7]} and of turbulence [2]} on phytoplankton life cycles. A unifying framework for different previous theories invoking the importance of the water-column depth and of turbulence intensity emerged from the influential work of Huisman and collaborators on sinking phytoplankton dynamics [9]}, [10]}.
Such previous studies, however, focused on the one-dimensional (1D) dynamics along the vertical, assuming that turbulence can be approximated by a diffusive process. Therefore, they could not account for the effects due to its complex, multiscale, character. In addition, persistent and well organized two-dimensional (2D) fluid motions, as those characterizing winter convection, were also suggested to play an important role on phytoplankton survival [11]}, [12]}.
